Question

Suppose that f(x) is continuous on [2,4] and f'(x) exists on [2,4] and f'(C)= f(4)-f(2)/2, then C is in (2,4). T or F? Justify your answer

Answer 1

have you heard of the mean-value theorem?

Answer 2

yes,

Answer 3

well, this is exactly the MVT (mean-value theorem), isn't it?

Answer 4

yes, but im not sure how to justify the answer

Answer 5

the MVT is justification

Answer 6

ok thanks,, quick question f(X) = x/2-x derivation is f'(X)= -1x(2-x)^-2 (-1)

Answer 7

is it\[f(x)=\frac{ x }{ 2-x }\]

Answer 8

yeah

Answer 9

so use the quotient rule, yeah?

Answer 10

no but using the rule i got this f'(X)= -x(2-x)^-2 + (2-x)^-1

Answer 11

\[f'(x)=\frac{ 1\cdot \left( 2-x \right)-x \cdot \left( -1 \right) }{\left( 2-x \right)^2 }=\frac{ 2-x +x }{\left( 2-x \right)^2}=\frac{ 2 }{\left( 2-x \right)^2}\]

Answer 12

got it

Answer 13

thanks

Answer 14

you're welcome